39tn aiaa/asme:/sae/asee joint
Propulsion Conference and Exhibit
Hunisville, AL
20-23 July 2003
AIAA-2003-4919
Calculation of Turbine Axial Thrust by Coupled CFD Simulations of the Main
Flow Path and Secondary Cavity Flow in an SLI LOX Turbine
D. J. Dorney
NASA/George C. Marsliall Space Flight Center
Space Transportation Directorate
MSFC.AL 35812
Bogdan Marcu
Ken Tran
Scott Sargent
The Boeing Company
Rocl<etdyne Propulsion and Power
6633 Canoga Avenue
Canoga Park, CA 91309-7922
ABSTRACT
Each single reusable Space Launch Initiative
(SLI) booster rocket is an engine operating at a
record vacuum thrust level of over 730,000 Ibf
using LOX and LH2. This thrust is more than
10% greater than that of the Delta IV rocket,
resulting in relatively large LOX and LH2
turbopumps. Since the SLI rocket employs a
staged combustion cycle the level of pressure is
very high (thousands of psia). This high
pressure creates many engineering challenges,
including the balancing of axial, forces on the
turbopumps. One of the main parameters in the
calculation of the axial force is the cavity
pressure upstream of the turbine disk. The flow
in this cavity is very complex. The lack of
understanding of this flow environment hinders
the accurate prediction of axial thrust. In order to
narrow down the uncertainty band around the
actual turbine axial force, a coupled, unsteady
computational methodology has been developed
to simulate the interaction between the turbine
main flow path and the cavity flow. The
CORSAIR solver, an unsteady three-
dimensional Navier-Stokes code for
turtx)machinery applications, was used to solve
for both the main and the secondary flow fields.
Turbine axial thrust values are presented in
conjunction with the CFD simulation, together
with several considerations regarding the turbine
instrumentation for axial thrust estimations
during test.
Copyright ©2003 by the American Institute of Aeronautics
and Astronautics, Inc. No copyright is asserted in the United
States under Title 17, U.S. Code. The U.S. Government has
a royalty-free license to exercise all rights under the copyright
claimed herein for Governmental Purposes. All other rights
are reserved for the copyright owner.
INTRODUCTION
In the recent years the harnessing of increased
computing power through parallelization of CFD
codes has allowed turtx)machinery engineers to
extend their analyses to the secondary flow paths
of turbomachines. The prediction of unsteady,
three-dimensional viscous flow physics using CFD
for the main compressor and turbine flow paths has
been coupled with the flow through disk and
housing cavities in an effort to better model and
understand the actual flow in a turbomachine.
One of the main motivations for the analysis of the
secondary flow paths has been the necessity to
understand and quantify the heat transfer and
cooling capacities of such flows, as well as the
perfonnance impact the designer must pay in order
to use such capacities. Early works in addressing
cavity flows [1-4] was driven by the need to
understand the cooling cavity flows in basic
geometries. The early numerical results reported in
the literature [such as Refs. 5 and 6, among an
exhaustive list of valuable contributions] have been
based on 2-D, steady flow models that do not
completely account for the complex environment of
rotor-stator interaction coupled with the cavity flow
field. Recently [7], results of more complex
simulatk>ns have been reported. Such simulations
are based on the coupling of large and well-
validated CFD solvers for simultaneous calculations
of the turbine main flow path (e.g., NASA MS-
TURBO) and the cavity flow field (e.g., NASA
SCISEAL). Special attention is focused on grid
onautics and Astronautics
AIAA-2(X)3-4919
issues and solving the flow accurately though
the seal packages.
While a wealth of information pertaining to the
flow of cooling streams in the disk cavity
geometries typical to air-breathing gas turbine
engines has been, and is being, delivered by the
contributions of numerous authors, less data is
available for the disk cavity geometries typically
encountered in the turbopumps equipping liquid
propellant rocket engines. Such geometries
have the same level of complexity as the gas
turbine engines, but a more severe operating
environment. Typically, cryogenic turbopump
turbines operate in a hot, high-pressure gas
environment, separated by inches from the
cryogenic fluid flow path of the pump. If the
pumped fluid and the turbine working fluid are
compatible, small quantities of cold vaporized
fluid from the pump secondary flow paths may
be allowed to leak into the turbine cavity. The
cold net inflow mixes with hot gas in the cavity in
a manner that is not currently understood. If the
fluids are not compatible (for example, in a liquid
oxygen turbopump powered by gaseous hot
hydrogen) the turbine cavity and the pump
secondary flows must be carefully organized to
keep the fluids separated. One way to achieve
separation is through an interstage seal that
allows each leakage to drain out. The turbine
cavity in this case has a net outflow.
In the latter example of a design configuration, a
significant uncertainty arises for the case of very
large turbopumps; namely the magnitude of the
axial thrust produced by the turbine disks. The
energetic nature of pump operation requires a
carefully organized balance between the axial
loads produced on the pump and turbine rotating
components.
The present paper specifically addresses this
uncertainty as related to the Space Launch
Initiative RS-83 Engine Liquid Oxygen
turt)opump via coupled CFD simulations in
which both the turbine main flow path and the
cavity flow are simultaneously solved in the full
three-dimensional, viscous unsteady regime.
The cavity net flow, pressure distribution and
resulting axial thrust are calculated for three
situations, corresponding to a well sealed cavity
with minimum mass flow leaking into the drain
system, and two cavities with increased levels of
wear for the seals.
LOX TURBINE AERODYNAMIC DESIGN
The oxidizer turbopump (OTP) turbine for the
Boeing Rocketdyne RS-83 hydrogen fueled engine
is a single stage, subsonic design. The primary
design objectives for this turbine are high
performance and robust design. To satisfy these
conditions the turbine achieves an efficiency of
77% at the design pressure ratio (PR) of 1.22.
Turbine design total inlet pressure is 3876 psia.
The turbine has a relatively large pitch line diameter
of 16.21 in. with a blade height to diameter ratio
(L/D) of 8.9% and a throat aspect ratio (L/O) of
4.69. While the pitch diameter of the turbine is
large, the operation of the seal package preventing
excessive mass flow leakage out of the turbine
cavity imposes a low diameter size for the seal.
Consequently, the turbine disk offers a large area
for the cavity pressure to act upon and produce
axial load. The understanding of the cavity flow and
the associated pressure distribution becomes a
strong requirement for a robust design.
NUMERICAL PROCEDURE
The governing equations considered in this study
are the time-dependent, three-dimensional
Reynolds-averaged Navier-Stokes equations. The
numerical algorithm used in the computational
procedure consists of a time marching, implicit,
finite-difference scheme. The procedure is third-
order spatially accurate and second-order
temporally accurate. The inviscid fluxes are
discretized according to the scheme developed by
Roe [8]. The viscous fluxes are calculated using
standard central differences. An approximate-
factorization technique is used to compute the time
rate changes in the primary variables. Newton sub-
iterations are used at each global time step to
increase stability and reduce linearization errors.
The equations of motion are extended to turbulent
flows using an eddy viscosity formulation. The
turbulent viscosity is calculated using the two-layer
Baldwin-Lomax algebraic turbulence model [9].
Message Passing Interface (MPI) and OpenMP
directives have been implemented into the code to
reduce the computation time for large-scale three-
dimensional simulations. The use of MPI allows the
coupling of different geometric components, such
as the turbine main flow path and cavity, in a
straightfonward manner. This procedure was
previously demonstrated for unsteady flow in a
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
supersonic turbine
nozzles [10].
with straight centerline
The computational procedure uses O- and H-
type zonal grids to discretize the flow field and
facilitate relative motion of the rotating
components. The 0-grids are body-fitted to the
surfaces of the airfoils and generated using an
elliptic equation solution procedure. They are
used to properly resolve tfie viscous flow in the
blade passages and to easily apply the algebraic
turbulence model. The algebraically-generated
H-grids are used to discretize the remainder of
the flow field, including the turbine cavity.
Figure 1 shows an axial cut through the
computational grids. The turbine is modeled as a
53 nozzle/53 blade turbine (1/1 computationally)
using 111x45x31 (H) and 121x45x31 (O) grids
for nozzle, and 111x45x31 (H) and 121x45x31
(O) grids for rotor. The cavity is modeled using a
35x45x1 1 1 (H) grid.
The circumferential span of the computational
domain is 6.8 ".
The computational analysis has been validated
on several rocket-engine turbine geometries,
including coupled components such as straight
centeriine nozzles (e.g., Refs. 10-14).
Boundary Conditions
The theory of characteristics is used to
determine the boundary conditions at the inlet
and exit of the computational domain. For
subsonic inlet flow the total pressure, total
temperature, and the circumferential and radial
flow angles are specified as a function of the
radius. The upstream running Riemann
invariant, is extrapolated from the interior of the
computational domain.
For subsonic outflow the circumferential and
radial flow angles, total pressure, and the total
temperature are extrapolated from the interior of
the computatignal domain. For the turbine main
flow path the totai-to-static pressure ratio is
specified at mid-span of the computational exit
and the pressure at all other radial locations at
the exit is obtained by integrating the equation
for radial equilibrium. For the cavity flow, the
upper computational domain is coupled with the
main flow computational domain at the H-grid
area corresponding to the turbine nozzle hub
wall. The cavity walls are one stationary and one
rotating with so slip boundary conditions enforced
on each.
Given the relatively large size of the grid, the
labyrinth seal is not modeled numerically, as such
additional modeling would have rendered the study
computationally too expensive. Instead, the degree
of wear in the seal is modeled through a pressure
drop across the discharge area at the bottom of the
cavity, with the largest the pressure drop
corresponding to the most extensive wear modeled.
The objective of the calculation is to model the
cavity flow at progressively larger mass flow rates.
Periodicity is enforced along the outer boundaries
of the H-grids in the circumferential direction. For
viscous simulations, no-slip boundary conditions
are enforced along the solid surfaces. It is
assumed that the norrrial derivative of the pressure
is zero at solid wall surfaces. In addition, a
specified (zero) heat flux is held constant in time
along the solid surfaces.
Figure 2 shows an instantaneous snapshot of the
confluence of the two computational domains and a
vector flow visualization of the flow pattem as mass
flow is captured by the cavity volume.
RESULTS
The results presented in this report are
circumferentially and time averaged unless
specified otherwise. Of interest is the radial
distribution of pressures p=p(r) for the three
different flow regimes considered. Table 1
presents the mass flow values for t>oth the cavity
and the turbine flow path for the three regimes
denoted as Low Flow (which is the nominal flow as
per design), Medium Flow and High Flow. All
denoted values refer to the mass flow leaked at the
bottom of the cavity. The algebraic sum of mass
flows is not conserved from one case to another:
the turbine boundary conditions, which are inlet
pressure and temperature and inlet total to exit
static pressure ratio, together with the coupling of
the secondary cavity flow generate slightly different
flow mass values entering the turbine nozzle. Thus,
there is some overall variation in the turbine mass
flow between the different cases. The variation,
however, is less than one tenth of one percent.
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
Table 1 Mass flow values for the three cases
Gbm/s)
Case
Low Flow
Med Flow
Higli Flow
Turbine
257.4
256.7
256.9
Cavity
3.5
4.8
8.1
Figure 3 shows the radial pressure distribution in
the cavity for the three cavity mass flows. The
average cavity pressure decreases proportional
to the pressure drop across the discharge area
at the bottom of the cavity and increasing mass
flow. The shape of the radial pressure
distribution curve also changes slightly. The fast
pressure drop at the top of the cavity for all three
cases is explained by examining the vector plot
of the cavity flow field in Fig. 4. At the upper lip
of the cavity the entering flow forms a stagnation
area followed by a downward accelerated flow
along the rotating disk wall. The "hump" in all
three curves at a radius between 5.75 inches
and 6 inches is due to the local geometry (locally
increased volume) of the cavity.
Table 2 lists the axial loads produced on the
turbine disk by the three pressure distributions
shown in Fig. 3. The values are calculated by
it max
F = 2;r jp(r)rdr-^l^P,,
(1)
Rima
where p(r) is the radial pressure distribution, Rmm
and Rmax are the radii at the top and bottom of
the cavity, and Pexu is the turbine discharge
pressure
Table 2. Axial load on the turbine disk
(values in Ibf)
Case
Low Flow
Med Flow
High Flow
F
-17904.1
-19121.7
-21751.9
F%
variation
±3.2%
±3.4%
±4.9%
The percent variation in axial thrust is due to
significant fluctuation in the pressure distribution
values for each case. Figures 5a, 5b and 5c
show each of the p = p(r) curves from Fig. 3, as
well as it's fluctuation range. The authors did not
identify a strong correlation between the rotor
blade position and the pressure fluctuation. If
such a correlation existed, clocking effects for
each cavity sector (of which only a 6.8° period
section is modeled here) in relation to the rotor-
stator ir^tantaneous position may reduce the
percentage variations shown |n Table 2. However,
no such correlation has been identified, the
pressure variations shown in Fig. 5 being a
combined effect of variations in pressure at the
upper lip of the cavity and compressibility effects.
The pressure distribution p = p(r) is never available
when testing hardware, the price and complexity of
the instrumentation would be prohibitive. A
common practice is to model the pressure variation
in the cavity based on a swirling flow model and
compute a pressure distribution anchored on the
pressure value at the lip of the cavity p(rma)^, which
is known at design time from the turbine mean flow
path analysis:
Pir^)-P^r)= — — (2)
IglAA
where p is the fluid density, £2 is the turbine angular
velocity (in radians per second), g is the
gravitational constant, and k is what is usually
called as the pumping coefficient or slip factor
coefficient
(3)
The pumping coefficient is a way to estimate how
much of the disk tangential velocity U is imparted to
the fluid velocity, Cu.
The true values of the k factor at each radius k=k(r)
are shown in Fig. 6. If one were to use these
values (smoothed) and compute the radial pressure
distribution in the cavity using expression (2), the
results would look as shown in Fig. 7. Clearly, at
least for the geometry analyzed here, the swirling
flow model is not quite accurate.
In practice, for turbopump development testing one
or several redundant pressure sensors are placed
in the cavity at one particular radius. The choice of
where to place the sensors depends on the practice
of the team, the availability of space to place the
sensor itself, or other particular issues. Figure 8
shows the cavity analyzed in this study and four
radial locations at which a static pressure sensor
may be placed. These are four distinct possibilities.
For each of these test configurations, the local
pressure p(rprobe) value is used to calculate a value
for the k factor using Eqn. (2). Then, also using
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
Eqn. (2) and the freshly calculated k factor, a
radial pressure distribution is calculated, and
integrated to obtain the axial disk load. Figure 9
shows the comparison between the radial
pressure distributions shown in Fig. 3 and the
pressure distributions obtained based on the
four static pressure measurement points, for
each flow case. With the exception of the top
portion, the radial pressure distribution is
matched well for the cases when the choice is to
place the pressure sensor at mid-to-lower radii
rather than higher radii in the cavity. Optimum
for the present case is the KP2 location at the
5.75 in radius, which is also the location of the
bulkier local volume in the cavity geometry. This
observation is valid for the cavity geometry at
hand, but a generalization cannot be made
without analyzing a large number of other
geometries of cavities. Table 3 lists the values
for the axial turbine disk loads computed for the
pressure distributions shown in Fig. 9 using
expression (1).
Table 3. Turbine disk axial loads (Ibf).
Case
Low Flow
Med Flow
High Flow
F(lbf)
%err
F(lbf)
%err
F(lbf)
%err
KP1
-19785
10.5
-20957
9.6
-24538
12.8
KP2
-17611
1.6
-19106
0.1
-21282
2.1
KP3
-17485
2.3
-18467
3.4
-20660
5.0
KP4
-17185
4.0
-18260
4.5.,
-20495
5.8
Summarv and Conclusions
A series of numerical simulations have been
periomied for a coupled turbine/cavity geometry.
The simulations were performed for three
different leakage rates and levels of wear. The
predicted results differed from traditional swirl
models, but provide valuable insight into the
production of the turbine disk axial thrust loads.
The application of a CFD analysis to determine
sensor placement locations in turbine cavities
was demonstrated.
2. Northrop, A., and Owen, J. M., "Heat-Transfer
Measurements in Rotating Disk Systems, Part
2: The Roating Cavity with Radial Outflow of
Cooling Air." Int. J. Heat and Fluid Flow, Vol.9,
pp.27-36, 1988
3. Chew, J.W., and Rogers, R.H., "An Integral
Method for the Calculation of Turbulent Forced
Convection in a Rotating Cavity with Radial
Outflow", Int. J Heat and Fluid Flow, Vol.9
pp.37, 1988.
4. Graber, D.J., Daniels, W,A., and Johnson, B.V.,
"Disk Pumping Test:, AFWAL-TR-87-2050,
1987.
5. Virr, G.P., Chew, j. W., and Coupland, J.,
"Application of CFD to Turbine Disk Cavities", J
Turtwmachinery, Vot.116, pp.701 -708, 1994.
6. Athavale, M.M., Przekwas, A.J., Hendricks,
R.C. and Steinetz, B.M., "Numerical Analysis of
Intra Cavity and Power-Stream Flow Interaction
in Multiple Gas-Turbine Disk-Cavities", ASME-
95-GT-325, 1995.
7. Athavale, M.M., Steinetz, B.M. and Hendricks,
B.M., "Gas Turbine Primary-Secondary
Flowpath Interaction: Transiend, Coupled
Simulations and Comparison with
Experiments", AIAA-2001-3627, 2001.
8. Roe, P. L, "Approximate Riemann Solvers,
Parameter Vectors, and Difference Schemes,"
Journal of Computational Physics, Vol. 43,
1981, pp. 357-372.
Baldwin, B. S., and Lomax, H., "Thin Layer
Approximation and Algebraic Model for
Separated TuriDulent Flow," AIAA Paper 78-
257, Huntsville, AL, January, 1978.
10. Griffin, L W. and Dorney, D. J., "Simulations of
the Unsteady Flow Through the Fastrac
Supersonic Turbine," ASME Journal of
Turbomachinery, Vol. 122, No. 2, April, 2000,
pp. 225-233.
References
1. Gan, X., Kilic, M., and Owen, J. K, "Flow
Between Counterrotating Disks", J.
Turbomachinery, Vol. 117, pp.298-305,
1995
11. Domey, D. J., Griffin, L W., and Huber, F., "A
Study of the Effects of Tip Clearance in a
Supersonic Turtsine," ASME Journal of
Turbomachinery, Vol. 122, No. 4, October,
2000, pp. 674-673.
American Institute of Aeronautics and Astronautics
AIAA-2(X)3-4919
12. Dorney, D. J., Griffin, L W., Huber, F.,
Sondal<, D. L., "Effects of Endwali
Geometry and Staci<ing on Two-Stage
Supersonic Turbine Performance," AIAA
Joumal of Propulsion and Power, Vol. 18,
No. 6, November-December, 2002, pp.
1305-1308.
13. Domey, D. J., Davis, R. L., Sharma, O. P.
"Unsteady f^^ultistage Analysis Using a
Loosely Coupled Blade Row Approach".
Journal of Propulsion and Power, Vol 12, Nr.
2, P274-282, 1996.
14. Sondak, D. L., and Dorney, D. J., "Vortex
Shedding in a Turbine Cascade",
International Journal of Turbo and Jet
Engines, 16, p 107-126, 1999.
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AIAA-2003-4919
Cavity
Figure 1 . The Computational grid
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AIAA-2003-49I9
Figure 2. Interface between the turbine main flow path and cavity flow: fluid is being ingested into the
cavity.
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
3370
3380 3390
Pressure - Psi
3400
3410
3420
Figure 3. Radial pressure distribution in tiie cavity.
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
7
1 ■ • '^.jjfc
6.5
6
-■.■■■■ ■■^S
5.5
5iTT=5
5
■ p^':r
4.5
.::■■:■■ ■;-■ .
4
-r:r:=: -
3.5
3
L — J
2.5
■ «■ ■
0.5 1
2.5-
0.40.60.8 1 1.2
0.20.40.60.8 1 1.2
a) b) c)
Figure 4. Cavity flow field for a) Low Flow b) Medium Flow and c) High Flow cases
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AIAA-2003-4919
-T 1 r-
AnsM'Pi
-^/-V-V-
ifiSiih
^®
V=^=-?JL-J
vSH
'US
ilittlk
C=>X=
pfyvi
:WSti.
-5-5557 '
w«
-X^X
^^m
^^^r;-
s;^^
^Sfflsffi
-ScSB^?
SfiS
-'-"-"-"'"- rV^y^V--
:====ff?2^elli
i=Si=;
----=^-J^J= Vi^_--"- -_-
--V.---."
_I I 1 I L_
330 ]» 3(011 MX M 3C9
ntsut'N
a)
b)
c)
Figure 5. Cavity radial pressure distributions and the associate ranges of variations for a) Low Flow, b)
iVIedium Flow and c) High Flow.
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
(1
C
w 5
3 ^ \
0.05
Low Flow
— Med FLOW
High Flow
I 1 Ml|||llll '" ■
J_
0.1 0.15
Pumping factor K value
0.2
0.25
Figure 6. Radial distribution of K factor values. K = Cu/U.
American Institute of Aeronautics and Astronautics
AIAA-2003-4919
7.5
7
6.5
6
5.5
5-
Q: 4.5
4--
3.5 -
3-
2.5 -
o;
m.
— LowRowP(r)
— Med FLOW p(r)
High Flow p(r)
c Low Flow K-P(r)
o Med Flow K-P(r)
o High Flow K-P(r)
_i_
I ! I r
^ ^'^
^^■^^r6 ■•&
<->
_1_
3330 3340 3350 3360
3370 3380
Pressure -Psi
3390 3400 3410 3420
Figure 7. Comparison between cavity radial pressure distributions as computed from the CFD flow
solution and from the swirl flow model. The K factor values from figure 6 have been used, after
smoothing.
American Institute of Aeronautics and Astronautics
KPl
KP2
KP3
KP4
AIAA-2003-4919
2.5
mmimmA
'IttiiniunfiiFi
'IIIISSJKKS'
iisaisis
iiuii iinii ifiu'.'i)
AU III II IMIIi'J
Wft\nnHii nm:
•>fflH«i II nmii
\ omm ir im.-
L iiijiuil II Jiifi: '
ii Hill iiiiiiii mU'..
1 iiiii Ml mm>\ I
'mill mrnvK [
iM \\)\r
0.5 1
Figure 8. Pressure sensor probe locations.
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AIAA-2003-4919
c
i s
■
u
u
i
2S
U»Ftt»W
-1 1 1 1 1 i !—
tmrn-H
a)
b)
c)
Figure 9. Cavity radial pressure distribution calculated based on the various K factors anchored based on
pressure measurement at the four KP points shown in figure 8.
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